Stokes formula for Banach manifolds
There are different generalizations of the Gauss-Ostrogradsky formula (a divergent version of the Stokes formula) \[ \int\limits_{S}\mathrm{\operatorname{div}}\boldsymbol{X}\,d\mu =\int\limits_{\partial S}\left( \boldsymbol{X},\boldsymbol{n}\right) \,d\sigma \] for infinite-dimensional and nonlinear cases [\textit{A. V. Skorokhod}, Integration in Hilbert space. Translated from the Russian by Kenneth Wickwire. Berlin-Heidelberg-New York: Springer-Verlag (1974; Zbl 0307.28010); \textit{H.-H. Kuo}, Gaussian measures in Banach spaces. Berlin-Heidelberg-New York: Springer-Verlag (1975; Zbl 0306.28010); \textit{A. V. Uglanov}, Integration on infinite-dimensional surfaces and its applications. Dordrecht: Kluwer Academic Publishers (2000; Zbl 0951.46044); \textit{Yu. V. Bogdanskii}, Ukr. Math. J. 64, No. 10, 1475--1494 (2013; Zbl 1287.58005); translation from Ukr. Mat. Zh. 64, No. 10, 1299--1313 (2012); \textit{Yu. V. Bogdanskii}, Ukr. Math. J. 70, No. 5, 702--718 (2018; Zbl 1499.26042); translation from Ukr. Mat. Zh. 70, No. 5, 611--624 (2018)]. This paper proposes a divergent version of the Stokes formula for a surface of finite codimension embedded in a Banach manifold.
scientific article; zbMATH DE number 7361380
scientific article